Measurement of the Weyl Potential Evolution and E G Statistic from KiDS-1000, BOSS and 2dFLenS

A recently developed model-independent approach to measuring the Weyl potential has shown some tensions with Λ CDM (Lambda Cold Dark Matter) in DES (Dark Energy Survey) Y3 data. We apply this framework to Kilo-Degree Survey (KiDS-1000) weak lensing and BOSS/2dFLenS galaxy clustering using the KiDS Cosmology Analysis Pipeline (KCAP) in two redshift bins. To apply this method to the BOSS spectroscopic wedges, we take the early-time power spectrum from a redshift where General Relativity (GR) is recovered and jointly fit the late-time observables,, and. With Planck18 priors, the CMASS measurement of is 1.50σ below the GR prediction, while the LOWZ measurement remains consistent with it. The decrease in the central value of from LOWZ to CMASS provides a mild indication of the previously reported ``Lensing is low'' behavior. Without Planck18 priors, we obtain E G(0.38)=0.503 plus or minus0.054 and E G(0.61)=0.444 plus or minus0.054, both consistent with GR. Furthermore, phenomenological gravity tests also show no significant preference for modified gravity.